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Journal of the London Mathematical Society 2000 62(1):107-116; doi:10.1112/S0024610700001058
© 2000 by London Mathematical Society
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© The London Mathematical Society

Continuity of Actions of Groups and Semigroups on Banach Spaces

Lawrence G. Brown

Department of Mathematics, Purdue University West Lafayette, IN 47907, USA lgb{at}math.purdue.edu

Received 4 December 1998.

It is shown that if a locally compact group acts isometrically on a Banach space X leaving a closed subspace M invariant, and if the induced actions on M and X/M are strongly continuous, then the action on X is strongly continuous. Since this may be of interest for one-parameter semigroups, similar results are proved for actions of suitable topological semigroups. Other generalizations are given for (suitable) non-isometric actions, non-locally compact groups, and non-Banach spaces; corollaries concerning 1-cocycles and uniformly continuous actions are given.


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